A new approach for modeling cellulase–cellulose adsorption and the kinetics of the enzymatic hydrolysis of microcrystalline cellulose

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Abstract
Two fractions of substrate in microcrystalline cellulose which differ in their adsorption capacities for the cellulases and their susceptibility to enzymatic attack have been identified. On the basis of a two-substrate hypothesis, mathematical models to describe enzyme adsorption and the kinetics of hydrolysis have been derived. A new nonequilibrium approach was chosen to predict cellulase–cellulose adsorption. A maximum binding capacity of 76 mg protein per gram substrate and a half-maximum saturation constant of 26 filter paper units (FPU) per gram substrate have been calculated, and a linear relationship of hydrolysis rate vs. adsorbed protein has been found. The fraction of substrate more easily hydrolyzed, as calculated from hydrolysis data, represents 19% of the total effective substrate concentration. This fraction is only slightly different from that of other celluloses and has been estimated to be 27% and 30% for NaOH- and H3PO4-swollen cellulose, respectively. The effective substrate concentration is equal to the maximum amount of the substrate which can be converted during exhaustive hydrolysis. This in turn is determined by the overall degradability of the substrate by the cellulases (85–90% for microcrystalline cellulose) and by the cellobiose concentration during hydrolysis. The kinetic model is based on a summation of two integrated first-order reactions with respect to the effective substrate concentration. Furthermore, it includes the principal factors influencing the reaction rates: the ratio of filter paper and β-glucosidase units per gram substrate and the initial substrate concentration. © 1993 John Wiley & Sons, Inc.